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Issue ESAIM: Proc.
Volume 19, 2007
Conference Oxford sur les méthodes de Monte Carlo séquentielles
Page(s) 18 - 21
DOI http://dx.doi.org/10.1051/proc:071904
Published online 30 October 2007

ESAIM: Proc., 2007, Vol. 19, pp. 18-21
DOI: 10.1051/proc:071904

An approximate McKean-Vlasov model for the stochastic filtering problem

Dan Crisan1 and Jie Xiong2

1  Department of Mathematics, Imperial College London, London SW7 2BZ, UK.
2  Department of Mathematics, University of Tennessee, Knoxville TN 37996-1300, USA.


(Published online: 30 October 2007)

Abstract
The solution of the stochastic filtering problem is approximated using Clark's robust representation approach [Proc. 2nd NATO Advanced Study Inst., Darlington, 1977, pp. 721-734]. The ensuing approximation is shown to coincide with the time marginals of solutions of a certain McKean-Vlasov type process. The result leads to a representation of the solution of the stochastic filtering problem as a limit of empirical distributions of systems of equally weighted particles. A similar representation has been introduced by Del Moral and Miclo in [Stochastic Process. Appl. 86 (2000), no. 2, 193-216.] in the context of Feynman-Kac formulae. The representation introduced below differs from the one introduced in [Del Moral and Miclo, Stochastic Process. Appl. 86 (2000), no. 2, 193-216.] as it involves processes with no jumps.



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